If your keyboard or mouse needs a wireless Bluetooth transceiver in order to connect to a computer, make sure that you install the transceiver's driver in the computer, which can be found on the CD which should be inlcuded in the wireless set, or alternatively, found on the manufacturer's website.
If you cannot pair your computer with another bluetooth-capable device (e.g. smartphone, tablet, bluetooth speaker/headphones, keyboard, etc.) restart the computer, after which you should be able to pair it.
If your device is powered by non-rechargeable batteries and you were unable to turn it on, consider replacing the batteries. To be 100% sure that the batteries need to be replaced, test them on another device which uses batteries of the same type.
Contact the device manufacturer's customer support
Maybe your device's bluetooth issue can be resolved easily by the manufacturer's customer support team. All you need to do is to call them and follow their instructions. Also, most of the manufacturers have a troubleshooting page on their websites, which can help you fix your device's bluetooth feature by yourself.
Verify that the other device's Bluetooth feature is enabled and functional
In order for a Bluetooth communication to be established, the Bluetooth feature should be enabled on both the devices. If it is enabled on both devices, but a communication isn't established and if you verified that your device's Bluetooth feature works, check if the other device's Bluetooth feature works, too. For example, try pairing the device to another device.
Note: If you determined that the other device's bluetooth doesn't work, restarting the device should make it work again.
If your Wi-Fi router is near the Bluetooth device(s) and you have issues with establishing a good Wi-Fi connection between them, move the devices away from the router. Wi-Fi routers might interfere with the Bluetooth signal as they work on the same frequency.
Make sure to be as far as possible from Wi-Fi routers if you want a strong Bluetooth connection.